Aiming at a type of vehicle routing problem with multiple time windows under fuzzy demand (VRPMTW_FD) that exists widely in reality, that is the customer demand is fuzzy before the vehicle is delivered, but the customer demand becomes definite after the vehicle reaches the customer, a fuzzy chance constrained programming model based on fuzzy credibility theory is constructed to minimize the total cost, and a two-stage hybrid optimization algorithm (TSHOA) is proposed to solve it. Firstly, the first stage of TSHOA designs an improved gray wolf optimization algorithm (IGWO) to solve the VRPMTW with fuzzy customer demand before vehicle delivery, to obtain the pre-optimized path of VRPMTW_FD. Then, in the second stage of TSHOA, the optimal point rescheduling strategy (OPRS) is proposed to dynamically adjust the pre optimized path, so as to determine the appropriate return point and reduce the additional cost caused by the failure of the pre optimized path due to the fuzzy customer demand. Through simulation experiments and algorithm comparisons on different scale problems, it is verified that TSHOA can effectively solve VRPMTW_FD.